A predictor-corrector deep learning algorithm for high dimensional stochastic partial differential equations
In this paper, we present a deep learning-based numerical method for approximating high
dimensional stochastic partial differential equations (SPDEs). At each time step, our method …
dimensional stochastic partial differential equations (SPDEs). At each time step, our method …
Numerical Computation for Backward Doubly SDEs with random terminal time
A Matoussi, W Sabbagh - Monte Carlo Methods and Applications, 2016 - degruyter.com
In this article, we are interested in solving numerically backward doubly stochastic
differential equations (BDSDEs) with random terminal time τ. The main motivations are …
differential equations (BDSDEs) with random terminal time τ. The main motivations are …
[HTML][HTML] Stochastic partial differential equations with singular terminal condition
A Matoussi, L Piozin, A Popier - Stochastic Processes and their …, 2017 - Elsevier
In this paper, we first prove existence and uniqueness of the solution of a backward doubly
stochastic differential equation (BDSDE) and of the related stochastic partial differential …
stochastic differential equation (BDSDE) and of the related stochastic partial differential …
A nonintrusive stratified resampler for regression Monte Carlo: Application to solving nonlinear equations
E Gobet, G Liu, JP Zubelli - SIAM Journal on Numerical Analysis, 2018 - SIAM
Our goal is to solve certain dynamic programming equations associated to a given Markov
chain X, using a regression-based Monte Carlo algorithm. More specifically, we assume that …
chain X, using a regression-based Monte Carlo algorithm. More specifically, we assume that …
Probabilistic interpretation for solutions of fully nonlinear stochastic PDEs
In this article, we propose a wellposedness theory for a class of second order backward
doubly stochastic differential equation (2BDSDE). We prove existence and uniqueness of …
doubly stochastic differential equation (2BDSDE). We prove existence and uniqueness of …
An implicit numerical scheme for a class of backward doubly stochastic differential equations
In this paper, we consider a class of backward doubly stochastic differential equations
(BDSDEs for short) with general terminal value and general random generator. Those …
(BDSDEs for short) with general terminal value and general random generator. Those …
Numerical computations for Backward Doubly Stochastic Differential Equations and Nonlinear Stochastic PDEs
A Bachouch - 2014 - theses.hal.science
The purpose of this thesis is to study a numerical method for backward doubly stochastic
differential equations (BDSDEs in short). In the last two decades, several methods were …
differential equations (BDSDEs in short). In the last two decades, several methods were …
[PDF][PDF] Equations rétrogrades avec singularités et autres contributions au calcul stochastique
A Popier - 2021 - hal.science
This document is a synthesis of the research that I have been conducting, along with my co–
authors, since the defense of my PhD thesis. This includes several topics, which are …
authors, since the defense of my PhD thesis. This includes several topics, which are …
Probabilistic interpretation for solutions of fully nonlinear stochastic PDEs
A Matoussi, D Possamai, W Sabbagh - arXiv preprint arXiv:1412.5548, 2014 - arxiv.org
In this article, we propose a wellposedness theory for a class of second order backward
doubly stochastic differential equation (2BDSDE). We prove existence and uniqueness of …
doubly stochastic differential equation (2BDSDE). We prove existence and uniqueness of …
-regularity result for solutions of backward doubly stochastic differential equations
A Bachouch, A Matoussi - Stochastics and Dynamics, 2020 - World Scientific
We prove an L 2-regularity result for the solutions of Forward Backward doubly stochastic
differential equations (F-BDSDEs) under globally Lipschitz continuous assumptions on the …
differential equations (F-BDSDEs) under globally Lipschitz continuous assumptions on the …